随机子空间法

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摘要-I-结构环境振动模态参数识别随机子空间方法与应用摘要环境激励振动试验,具有无须贵重的激励设备,不打断结构的正常使用,方便省时等显著的优点,更符合土木工程结构的实际使用特点。由于环境振动试验仅测量结构振动响应的输出数据,模态参数识别是仅基于输出数据的识别,不同于传统的基于输入和输出的模态分析,成为工程结构系统识别十分活跃的研究课题。本文对目前先进的数据驱动式随机子空间识别(SSI)的理论、算法、系统定阶、实桥应用进行了深入的探讨。完成的主要工作和结论包括:1.介绍了数据驱动的随机子空间识别理论和算法,重点讨论了对投影矩阵加权方法的不同导致的三种随机子空间识别算法:UPC法,PC法和CVA法。通过对西宁北川河桥环境振动实测数据的处理,分析了这三种方法的异同点。计算结果表明,三种算法相似,计算结果也很接近,从精度上讲,PC法会稍好,但相应的计算时间也长些。2.利用奇异熵的概念,提出和建立了用奇异谱分析技术和奇异熵增量的导数来实现数据驱动随机子空间识别方法系统定阶的方法和过程。用四层框架仿真算例和简支梁试验数据验证了所提系统定阶方法的可靠性。3.详细介绍了江西吉安大桥成桥环境振动试验,用随机子空间识别方法得到了该桥工作状态全桥桥面竖向、横向、纵向空间振动特性以及拱肋竖向、横向的振动特性。试验结果表明,用环境振动相应数据足以识别出该桥主要阶次的模态及其模态参数。利用所提出的奇异熵增量谱方法对吉安桥实测数据进行了系统阶次的确定,结果表明该法定阶稳定,可以避免系统定阶的盲目性。4.建立了江西吉安大桥的空间有限元模型,比较分析了有限元模态分析和试验模态分析的结果。有限元计算与实测结果吻合良好,表明所建立的吉安大桥有限元模型可以很好地预测该桥的动力学特性,可作为该桥各种复杂动力响应分析、长期健康监测和使用状态评估的基础。关键词:环境振动,模态参数识别,随机子空间识别,桥梁结构ABSTRACT-II-StochasticSubspaceIdentificationandApplicationofStructuresunderAmbientVibrationAbstractDynamictestingofstructuresunderambientvibrationexcitationhasmanyadvantages,suchasnoexcitationequipmentneeded,nointerruptionofstructuralserviceconditionsandlesstesttime,whichismoreclosetotherealworkingconditionsofcivilengineeringstructures.Asonlyoutputismeasuredandrealinputremainsunknownintermsofambientvibrationtesting,themodalparameteridentificationthereforebasesstructuraloutput-onlydata.Theoutput-onlymodalparameteridentificationisdifferentfromtraditionaloneandisnowveryactiveresearchtopicinthesystemidentificationofengineeringstructures.Thestate-of-the-artstudiesarecarriedoutinthisthesisonthetheory,algorithm,systemorderdeterminationandrealcaseapplicationsofthedata-drivenstochasticsubspaceidentification(SSI).Themainworkandconclusionsinclude:1.Thetheoreticalbackgroundofthedata-drivenstochasticsubspaceidentificationisdiscussed.Thestudyisfocusedonthreealgorithms:UnweightedPrincipalComponent(UPC)Algorithm,CanonicalVariateAlgorithm(CVA)andPrincipalComponentAlgorithm(PC)duetothedifferenttreatmentsontheprojectedmatrixofSSI.Theambientvibrationmeasurementsonarealcasearchbridge-BeichuanBridgeinXilin,China,areusedtocomparethemodalparameteridentificationresultsobtainedfromthreealgorithms.Itisdemonstratedthatthesethreealgorithmsareclosetogether.Intermsofidentificationaccuracy,thePCalgorithmisthebestbutitisalsotimeconsuming.2.Howtodeterminethesystemorderissofarstillaproblemamongtime-domainsystemidentificationtechniques.Basedontheconceptofsingularityentropyinthisthesis,thesingularityentropyincrementanditsderivativeareproposedtodeterminethesystemorderincorporatedwiththestochasticsubspaceidentification.One4-stroryframeandonesimplybeamareusedtodemonstratetheapplicabilityandreliabilityofproposedsingularityentropybasedmethods.3.ThefieldambientvibrationtestsontheJianarchbridgeinJiangxiProvinceisdescribedindetails.ThestochasticsubspaceidentificationhasbeenusedABSTRACT-III-successfullytoidentifythethree-dimensionalvibrationmodesofbridgedeckandarchribs.Itisdemonstratedthatthebridgeambientvibrationmeasurementsareenoughtoidentifythedominatedvibrationmodesofsuchalarge-scalebridge.Inaddition,theproposedsingularityentropybasedmethodisimplementedtodeterminethesystemorderofJianbridge.Itisagainverifiedthattheproposedsingularityentropybasedmethodisstableinthedeterminationofsystemorder.4.Athree-dimensionalfiniteelementmodeloftheJianbridgeisestablishedinthethesis.Themodalanalysisresultsobtainedfromfiniteelementcalculationhavebeencomparedwiththoseidentifiedfromthefieldambientvibrationmeasurements.Agoodagreementhasbeenachieved.Thecalibratedfiniteelementmodelthatreflectsthebuilt-upstructuraldynamicpropertiescanbeservedasabaselinemodelinthesucceedingdynamicresponseanalysisundercomplicatedexcitations,long-termhealthmonitoringandstructuralconditionassessmentoftheJianbridge.Keywords:Ambientvibration,ModalParameterIdentification,StochasticSubspaceIdentification,Bridge目录IV目录第一章绪论...............................................................................................................................11.1模态分析和模态参数识别.................................................................................................11.2经典的模态参数识别方法.................................................................................................21.3环境振动模态分析.............................................................................................................31.4环境振动模态参数识别回顾.............................................................................................41.4.1峰值拾取法(Peak-pickingmethod)................................................................41.4.2频域分解法............................................................................................................51.4.3联合时频域方法....................................................................................................51.4.4时间序列分析法....................................................................................................51.4.5随机减量法..............................................................................................................61.4.6NExT法...................................................................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